We introduce a general-purpose meta-algorithm that allows an analyst to take
any of a broad set of estimators that are unbiased
in the non-private setting and produce a differentially private version that,
with high probability, is unbiased and produces valid confidence intervals.
In Section , we introduce
our framework which takes its general structure from the Sample-Aggregate approach
of [1]}.
We use the Bag of Little Bootstraps (BLB) algorithm (Algorithm  [2]})
to approximate the sampling distribution of the non-private estimator
and privately estimate the parameters of said distribution using a modified
version of the CoinPress mean estimation algorithm (Algorithm  [3]}).
Under a few assumptions on the behavior of the bootstrap and initial user bounds,
our use of CoinPress produces unbiased parameter estimates
(Theorem REF ).
The estimated parameters and knowledge of the privatization process are combined to generate
final private mean and covariance estimates
(Theorems REF ,  REF , and REF ),
and valid confidence intervals
(Theorem REF , and
Corollary REF )).
We credit [4]} for first noting the compatibility of BLB with
Sample-Aggregate.
